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On the Adsorption Kinetics of Surface-Chemically Pure n-Dodecanoic Acid at the Air/Water Interface Alissa J. Prosser,† Utz Retter,‡ and Klaus Lunkenheimer*,† Max Planck Institute of Colloids and Interfaces, D-14424 Potsdam, Germany, and Federal Institute for Materials Research and Testing, Richard-Willstatter-Strasse 11, D-12489 Berlin, Germany Received September 16, 2003. In Final Form: January 7, 2004 The dynamic surface tension data for n-dodecanoic acid in 0.005 M hydrochloric acid, for as-received as well as for surface-chemically pure solutions, show the presence of a prolonged induction period, clearly indicating that the adsorption of this nonionic surfactant is not simply diffusion-controlled. A kinetic model for the reversible formation of monolayer islands, long known in the field of electrochemistry, is shown to also apply to the adsorption of n-dodecanoic acid at the air/water interface. The rate constant increases linearly with increasing bulk concentration, while the induction time decreases exponentially. The phenomenon of nucleation at the air/water interface is consistent with the direct experimental observation of the formation of solid-like patches as the interfacial region is drastically compressed.
1. Introduction Many novel adsorption properties were recently reported for n-alkanoic acids in 0.005 M hydrochloric acid at the air/water interface.1 The n-alkanoic acids with chain lengths nC < 11 revealed an adsorption behavior typical of soluble amphiphiles at room temperature. However, the surface properties of n-dodecanoic acid, though resembling those of the shorter-chain homologues in part, seemed to reveal also insoluble monolayer behavior, suggestive of a monolayer phase transition. Unfortunately, this question was not unambiguously answered because of certain experimental constraints. This paper focuses on the elucidation of the anomalous behavior of adsorbed monolayers of n-dodecanoic acid and in particular on the dynamic surface tension behavior, because it showed a very unusual feature, namely, a prolonged period of near constant surface tension. The presence of such an induction period has generally been attributed to a first-order phase transition within the adsorbed layer from a gaseous to a liquid-expanded state because of highly cooperative van der Waals interactions between the surfactant molecules.2-4 We propose a new type of analysis, an extension of the well-established nucleation and growth models used in electrochemistry for the characterization of phase transitions at the mercury/electrolyte interface. The thermodynamics of condensed adsorbates and the kinetics of the condensation have been extensively studied at the mercury/electrolyte interface.5-8 Most electrode condensates grow irreversibly from two-dimensional islands or clusters * Author to whom correspondence should be addressed. Phone: +49 (0)331 567 9445. Fax: +49 (0)331 567 9202. E-mail:
[email protected]. † Max Planck Institute of Colloids and Interfaces. ‡ Federal Institute for Materials Research and Testing. (1) Lunkenheimer, K.; Barzyk, W.; Hirte, R.; Rudert, R. Langmuir 2003, 19, 6140. (2) Lin, S.-Y.; McKeigue, K.; Maldarelli, C. Langmuir 1991, 7, 1055. (3) Ferri, J.; Stebe, K. J. Colloid Interface Sci. 1999, 209, 1. (4) Subramanyam, R.; Maldarelli, C. J. Colloid Interface Sci. 2002, 253, 377. (5) Retter, U. J. Electroanal. Chem. 1980, 106, 371. (6) Retter, U. J. Electroanal. Chem. 1984, 179, 25. (7) Philipp, R.; Dittrich, J.; Retter, U.; Mu¨ller, E. J. Electroanal. Chem. 1988, 250, 159. (8) Retter, U. Langmuir 2000, 16, 7752.
into a uniform close-packed film. An alternate, reversible mechanism was proposed to account for the presence of dynamically stabilized islands, which results in a steadystate surface coverage less than the maximal close-packed coverage.9,10 In electrochemistry, the differential capacitytime dependence at a given temperature is often used to evaluate the mechanism of the phase transition. In interfacial science, the surface tension-time dependence is used. Hence, we for the first time applied the relationships valid for surfactant adsorption at mercury/electrolyte interfaces to describe the dynamic surface tension of n-dodecanoic acid at the air/water interface and to judge, from it, about the question of phase transition. 2. Experimental Section 2.1. Materials and Sample Preparation. n-Dodecanoic acid (puriss., p.a., standard for gas chromatography) was obtained from Fluka. All water was twice-distilled. A laboratory stock solution of 1 M hydrochloric acid (Fluka) was available. All stock solutions were prepared in glass volumetric flasks and were shaken overnight. All dilutions were prepared in glass volumetric flasks and were allowed to equilibrate overnight. 2.2. Purification. Stock solutions of n-dodecanoic acid in 0.005 M hydrochloric acid were purified using the high-performance purification apparatus as described in ref 11 or were purified by hand. The automated cyclic procedure consists of compressing, aspirating, and expanding the adsorbed layer yielding a surfacechemically pure (scp) solution. In the manual procedure, the fully expanded adsorbed layer was aspirated with a suction pipet. The grade of scp was checked at given intervals by measuring the surface tension and applying the thermodynamic criterion derived in ref 12. 2.3. Surface Tension Measurements. Surface tension measurements were performed with a Lauda TE 1C tensiometer connected to an ABB Metrawatt chart recorder. A platinum Wilhelmy plate was used. All necessary precautions for this method were applied. The instrument dead time was estimated (9) Schrettenbrunner, M.; Chaiyasith, P.; Baumga¨rtel, H.; Retter, U. Ber. Bunsen-Ges. Phys. Chem. 1993, 97, 847. (10) Schrettenbrunner, M.; Chaiyasith, P.; Baumga¨rtel, H.; Retter, U. Ber. Bunsen-Ges. Phys. Chem. 1994, 98, 1501. (11) Lunkenheimer, K.; Pergande, H.; Kru¨ger, H. Rev. Sci. Instrum. 1987, 58, 2313. (12) Lunkenheimer, K.; Miller, R. J. Colloid Interface Sci. 1987, 120, 176.
10.1021/la035732u CCC: $27.50 © 2004 American Chemical Society Published on Web 03/03/2004
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to be less than 1 min. The resolution of the recorded surface tension was (0.2 mN/m. The tension was continuously monitored until the change in tension with time was less than 0.2 mN/m. The glass sample vessel (7.7 cm i.d., 2.8 cm height) was maintained at 295 ( 0.1 K using a Lauda RC6 circulating water bath. The sample solution was transferred from a volumetric flask to the sample vessel with a glass pipet. The air/solution interfaces were aspirated via pipet suction prior to each tension measurement. The surface tension of twice-distilled water was measured before and after each sample to ensure that ndodecanoic acid did not adsorb to the plate.
3. Theory 3.1. Diffusion-Controlled Adsorption Kinetics. The adsorption of nonionic surfactants at the air/water interface is generally characterized as diffusion-controlled based on the model of Ward and Tordai.13 A new method for the solution of the convolution integral derived by Ward and Tordai was recently presented.14 Thus, the determination of whether the mechanism of surfactant adsorption is diffusion-controlled should, in principle, be straightforward. However, the lack of reliable dynamic surface tension data often obscures the true adsorption mechanism. The few investigations in the literature for which the grade of scp was guaranteed, for simple surfactants such as alkanoic acids or dimethyl-n-alkylphosphine oxides, support a diffusion-controlled adsorption mechanism.12,14,15 As-received surfactant solutions are in fact mixtures of the surfactant under study along with traces of the hydrophobic parent compounds. Such trace impurities can retard the adsorption kinetics by several orders of magnitude.16 Chang and Franses17 correctly emphasize in their review that surface-active impurities not only influence the adsorption kinetics but also alter the equilibrium surface tension-concentration isotherm. The equilibrium model parameters extracted from the adsorption isotherm are used as inputs for dynamic diffusioncontrolled models. The importance of the equilibrium behavior in the understanding of the dynamic behavior of surfactant solutions has been recently underlined by Ferri and Stebe.18 When the surface coverage is low, the equilibrium surfactant distribution is well-represented by the linear Henry isotherm Γ ) KHc, where Γ is the adsorbed surface density, c is the bulk concentration, and KH is the Henry constant. For diffusion-controlled adsorption at a planar interface, consistent with the Henry isotherm, the normalized dynamic surface coverage θn is given by19
{ } {x }
Γ(t) D θn(t) ) ) 1 - exp 2 t erfc ΓE KH
D t K2H
(1)
where ΓE is the equilibrium surface concentration of the surfactant, D is the diffusion coefficient, and for KH is valid KH ) BΓm where B is the adsorption coefficient and Γm is the maximal possible surface concentration. 3.2. Dynamically Stabilized Islands Model. The kinetic process for reversible two-dimensional island (13) Ward, A. F.; Tordai, L. J. Phys. Chem. 1946, 14, 453. (14) Fang, J.-P.; Wantke, K.-D.; Lunkenheimer, K. J. Phys. Chem. 1995, 99, 4632. (15) Fang, J.-P.; Wantke, D.; Lunkenheimer, K. J. Colloid Interface Sci. 1996, 182, 31. (16) Lunkenheimer, K. In Encyclopedia of Surface and Colloid Science; Somasundara, P., Hubbard, A., Eds.; Marcel Dekker: New York, 2002; Vol. 1, p 3739. (17) Chang, C.-H.; Franses, E. I. Colloids Surf., A 1995, 100, 1. (18) Ferri, J.; Stebe, K. Adv. Colloid Interface Sci. 2000, 85, 61. (19) Bard, A.; Faulkner, L. Electrochemical Methods; Wiley: New York, 1980; p 518.
formation is described as follows: Molecules are deposited at the edges of monolayer islands. For instantaneous nucleation, all possible nuclei are already present at the very beginning of the adsorption film growth. For irreversible growth, the final film state is always the complete adsorption monolayer. When the formation of monolayer islands is reversible, there exists a dynamic equilibrium between the growth of the islands and desorption of island molecules from the interior of the islands to the bulk solution. The momentary degree of surface coverage of the adsorbed film is given by the double layer capacity C in electrochemistry or by the surface tension γ in surface science
Θf (t) )
CΘf )0 - C(t) CΘf )0 - CΘf )1
or
γo - γ(t) γo - γ∞
(2)
where γo is the surface tension of the pure solvent and γ∞ is the surface tension of the close-packed monolayer. The steady-state surface coverage of the condensed islands, for a given bulk concentration, is
Θi )
CΘf )0 - Css CΘf )0 - CΘf )1
or
γo - γss γo - γ∞
(3)
where γss is the steady-state surface tension. A normalized degree of coverage is then defined as
Θn(t) )
Θf (t) γo - γ(t) ) Θi γo - γss
(4)
The normalized coverage Θn does not represent a Gibbs surface density but rather the fraction of the film that is contained within the growing monolayer islands. In ref 9, the following model for the reversible formation of monolayer islands was derived. A constant number of equally sized circular monolayer islands grow at their edges by deposition of monomers. The growth rate is constant, i.e., the radius r increases proportional to the time. Furthermore, the desorption of molecules located inside the island is assumed to be proportional to the area of the island πr2. This results in the following equation for the differential change of the degree of coverage Θ1 of one island with time:
dΘ1 ) K(2rhkg - r2kd) dt
(5)
Here, K is a constant, h is the height of the monolayer, kg is the growth rate constant, and kd is the desorption rate constant. From the integration of this equation (see Appendix), one finally obtains the total momentary degree of coverage Θn of the condensed multi-island film
Θn(t) ) [1 - exp{-k2(t - ti)}]2
(6)
where k2 is proportional to the desorption rate kd and ti is the induction time. The induction time in nucleation is defined as the time at which the nucleation starts and not at which the phase transition is completed. At the end of the induction period, no further nuclei form in the case of instantaneous nucleation, but the nuclei continue to grow. Equation 6 can be rearranged to the following form:
ln{1 - xΘn(t)} ) -k2(t - ti)
(7)
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4.1. Solution Preparation and Purification. nDodecanoic acid in 0.005 M hydrochloric acid solution is slightly soluble and is known to be rather difficult to dissolve.21 The solubility limit of n-dodecanoic acid at room temperature is about 10-5 M.1 Stock solutions of concentrations ranging from 7 to 15 µM were prepared. A challenging result was obtained when the solutions were processed in the high-performance surface purification apparatus.11 The protocol for this apparatus consists of cyclicly aspirating an initially large adsorbed layer after it is drastically compressed to a surface area less than 4% of the initial value. However, the resulting surface tension increase after one siphoning was greater than that calculated under the assumption that the whole adsorbed layer of n-dodecanoic acid at the initial area had been completely removed. For example, the automated purification of an 8 µM stock solution resulted in an increase in the surface tension from 49 to 62 mN/m after only 12 cycles (i.e., 12 removals of the adsorption layer)! A careful check of these operations showed the following phenomenon: After the drastic compression of the adsorption layer, some tiny, irregular patches were visible on the surface. Thus, the strong compression of the adsorbed layer had obviously resulted in solidification of n-dodecanoic acid at the air/water surface. Consequently, the automated technique for the purification of the stock solution could not be applied. However, this solidification appeared to be reversible. The surface film would disappear when the solution was transferred into an overly large volumetric flask. It is important to emphasize that solidification was never observed in any solution at a constant surface area; i.e., it was never observed during a surface tension measurement. It was only observed during the drastic compression of the adsorbed layer (upward of 2000%) in the automated purification apparatus or in the neck of a volumetric flask, for solutions at or near the solubility limit. Thus, a new 500 mL stock solution of concentration 10 µM was prepared in a 1 L volumetric flask, carefully avoiding the narrow neck region. In this manner, the requisite experimental boundary conditions were properly observed. The stock solution was then carefully purified manually by aspirating the adsorption layer at different positions across a fully expanded surface. Hence, the principle of surface purification was maintained. In general, the surface tension increases with the number of purification cycles up to a plateau value as trace impurities, which concentrate at the interface, are removed from the solution. As the number of purification cycles continues to increase, a point is reached beyond
which purification begins to only remove the main component. The removal of the main component results in a linear relationship between the surface tension and the purification cycle number. For sparingly soluble surfactants such as n-dodecanoic acid, it is difficult to distinguish unambiguously between the removal of surfaceactive impurities and simple main component depletion because these two phenomena occur simultaneously. The surface tension of the n-dodecanoic acid solution was checked after every couple of purification cycles to judge the attainment of surface-chemical purity.12 In this case, it turned out that 5 cycles were sufficient (quite few compared to octanoic acid where 300 cycles were required22). The low number of purification cycles is a reflection of the low bulk concentration; however, because of the low concentration, even after 1 cycle, there was necessarily loss of the main component. The loss of the main component can be estimated from the purification characteristic. After 5 cycles, the surface tension had increased by 4 mN/m; this increase reflects a loss of both impurities as well as the main component. From the constant rate of surface tension increase with increasing cycle number for cycles above 5, it is estimated that 75% of the increase in tension for cycles 5 and under was due to the loss of the main component or that the concentration of the 10 µM stock is in fact closer to 7 µM. The removal of the main component is of course a concern, but the primary goal is the removal of surface-active impurities. 4.2. Surface Tension Measurements. The surface tension of a manually purified (five cycles) 10 µM stock solution was measured twice. The results were identical within the error of measurements. For this reason, and for clarity, error bars have been omitted from the figures. The stock solutions were diluted to the following (apparent) concentrations: 8.3, 6.8, 5.6, 4.6, and 1.5 µM. No adjustment to the concentration of the stock solution was made for the loss of the main component during the purification procedure. The surface tension of the five dilutions was measured after which a second dilution was prepared. The curves in Figure 1 show the surface tension-time dependence of scp n-dodecanoic acid for various concentrations ranging from the solubility to the limit of detection. Measurements for concentrations less than 3 µM were too noisy to evaluate over the long equilibration times (problems of water evaporation, random noise, etc.). In general, the transients are characterized by a concentration-dependent induction period of near constant surface tension at a value at or near that for the pure solvent. The steady-state tension of the base electrolyte solution, 0.005 M hydrochloric acid, at 22 °C was attained within the dead time of the instrument at a value indistinguisable from that for pure water (72.3 ( 0.2 mN/ m). From the inspection of Figure 1, the induction period varied in duration from under 1 min for the 10 µM solution to over an hour for the 3.6 µM solution and was followed by a more rapid decrease in the surface tension until a steady-state surface tension was achieved. The time at which the steady state was achieved decreased as the concentration increased. The surface potential as a function of time for n-dodecanoic acid has been previously reported.23 A direct comparison of the results in this paper to those in ref 23 is difficult because of the small solution thicknesses (4.6 and 2.3 mm) required for the surface potential measurements. An indirect comparison of the results shows a similar induction-type behavior that the diffusion-controlled model was unable to capture.
(20) Donner, C.; Baumga¨rtel, H.; Pohlmann, L.; Retter, U.; Philipp, R. Ber. Bunsen-Ges. Phys. Chem. 1996, 100, 403. (21) Petrov, P.; Joos, P. J. Colloid Interface Sci. 1996, 182, 179.
(22) Avranas, A.; Retter, U.; Lunkenheimer, K.; Lohse, H. J. Colloid Interface Sci. 1997, 189, 229. (23) Dudnik, V.; Lunkenheimer, K. Langmuir 2000, 16, 2802.
The model parameters k2 and ti are simply obtained from the linear regression of the rescaled dynamic tension data. Any two-dimensional instantaneous nucleation with induction time can be explained as follows: Up to ti, the surface coverage of the adsorbed molecules increases steadily in accordance with diffusion-controlled adsorption kinetics until a critical concentration necessary for nucleation is exceeded. Nucleation within the adsorbed layer is first balanced by continued adsorption from the bulk solution. As the nucleation and island growth proceed, the concentration at the surface can drop below the critical value and nucleation stops, but the islands continue to grow until a steady state is reached.20 4. Results and Discussion
Surface-Chemically Pure n-Dodecanoic Acid
Figure 1. Dynamic surface tension γ for aqueous solutions of scp n-dodecanoic acid in 0.005 M hydrochloric acid measured at 22 °C with the Wilhelmy plate for the indicated apparent bulk concentrations (µM). A logarithmic time scale is used to emphasize the duration of the induction period.
Figure 2. Comparison of the steady-state surface tension values for the scp n-dodecanoic acid solutions (0) shown in Figure 1 to as-received solutions (9). The lines are a quadratic fit to the data and are shown as a guide for the eye.
The surface tension transients shown in Figure 1 are different in form from those obtained using the du Nou¨y ring, possibly because of straining of the interface during the lifting of the ring.24 The dynamics observed with the ring were generally faster than those observed with the plate. With either technique, the dynamic surface tension could be described in three parts as follows: the induction period, rapid-fall period, and approach to a steady-state period. The steady-state values were in good agreement. The steady-state surface tension values for the dynamic data shown in Figure 1 are summarized in Figure 2. The steady-state surface tension decreases smoothly with an increasing bulk concentration up to the solubility limit. For purposes of comparison, the steady-state surface tension values for as-received n-dodecanoic acid solutions are also shown in Figure 2. The slope of the as-received surface tension-concentration curve is not as steep as that for the scp curve. 4.3. Evaluation of the Adsorption Kinetics. The induction time in the surface tension-time curves speaks (24) Lunkenheimer, K. Tenside Deterg. 1982, 19, 272.
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Figure 3. Normalized degree of coverage Θn as a function of time for the indicated n-dodecanoic acid concentrations (µM).
against the applicability of eq 1. Because that model and slightly more advanced models with Langmuir isotherm do not fit, this clearly indicates the presence of another controlling mechanism. There is no plausible physical reason that a diffusion process should include an induction time. This effect depends upon the nature of the adsorption isotherm and other assumptions built into or coupled to the diffusion equation. The main difference between our nucleation model and previous mass tranport models is the description of the state of the adsorbed layer after the induction period. Is it a single new continuous phase, or is it discontinuous? Our contention is that in fact it is discontinuous, with a network of islands. After the induction period, the nuclei grow until a steady-state size of the corresponding monolayer islands is attained. It is this growth of the nuclei that the model is designed to capture. Using eq 4, the surface tension transients shown in Figure 1 were converted into dynamic normalized coverages as shown in Figure 3. The step-shaped curves shown for a concentration of 3.6 µM are an artifact of the dataacquisition method. The tension was continuously measured and output to a chart recorder but was discretely transferred into a digital format at a resolution of 0.2 mN/m. The discrete nature of the data does not affect the conclusions drawn from them. For normalized coverages in the region 0.1 e Θn e 0.9, the Θn data were replotted according to eq 7 as shown in Figure 4. The rescaled tension data are quite linear and therefore are well-represented by the dynamically stabilized islands model. The model parameters k2 and ti were obtained directly from a linear regression. The correlation coefficients (R2) ranged from 0.999 (10 µM) to 0.974 (3.6 µM). For purposes of comparison, eq 6 was directly optimized using the Origin software package to obtain best-fit values for the four parameters γo, γss, k2, and ti. This direct optimization resulted in slightly more accurate parameter values for the lower concentrations, where the data were more discrete than continuous in nature. The model parameters obtained from the linear regession are shown in Figure 5. The value of the desorption rate k2 increases nearly linearly with the bulk concentration from 0.04 to 0.20 min-1. Note that the induction time is presented in a logarithmic scale. With increasing concentration, the rapidly decreasing induction time
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5. Conclusions
Figure 4. Normalized degree of surface coverage shown in Figure 4 linearized according to eq 7 in the range 0.1 e Θn e 0.9. The R2 values range from 0.999 to 0.974 as the concentration decreases and the data become more discrete in nature.
The adsorption of scp n-dodecanoic acid at the air/water interface was studied by dynamic surface tension measurements. All solutions contained hydrochloric acid to supress the dissociation of the fatty acid. Criteria for judging the purity of the solution were applied, with special attention toward the observed boundary conditions for the n-dodecanoic acid system. As a sparingly soluble surfactant, special care must be taken in the preparation, purification, and handling of the aqueous solution. Drastic changes in the surface area, such as in the neck of a volumetric flask or in the automated purification apparatus, must be avoided. The surface tension values for the purified solutions were quite different from those of the unpurified solutions, partly because of main-component losses during purification. Nonetheless, the slopes of the equilibrium adsorption isotherms significantly differ, highlighting the strong effect of even trace impurities on the adsorption process. The dynamic tension data are well-represented by the reversible formation of monolayer islands model, i.e., instantaneous two-dimensional nucleation with constant growth at the edges of circular monolayer islands and desorption of adsorbed molecules from the interior of the islands proportional to the island area. The model rate constant increases linearly with increasing bulk concentration, while the induction time decreases exponentially. Acknowledgment. This research was supported by Deutsche Forschungsgemeinschaft (Project LU455/4-1). We thank G. Wienskol for the manual purification of n-dodecanoic stock solutions. Appendix: Detailed Derivation of the Nucleation Model, Adapted from Reference 9 When the film growth is limited by the desorption of island molecules into the bulk solution, the overall rate of film growth is given by
dΘf π dV F ) (2rhkg - r2kd) ) dt SeΓm dt MSeΓm Figure 5. Regressed nucleation model parameters k2 (9) and ti (0) as a function of the bulk concentration. The lines are a guide for the eye.
indicates that the film formed faster, but this formation is counterbalanced by the increasing desorption rate. The presence of an induction period in the dynamic surface tension can be attributed to various factors and is not conclusive proof in and of itself of the presence of two-dimensional nucleation within the adsorbed layer. We consider the presence of the induction time, shape of the surface tension-concentration curve, goodness of fit of the nucleation model, eqs 6 and 7, all as strong evidence supporting our hypothesis. In the context of the nucleation model, the different steady-state surface tensions as a function of concentration indicate some form of reversible growth. The size of the growing islands determines the degree of surface coverage, while the size or radius of the islands is determined by kg and kd. Any “holes” resulting from desorption will be closed by contraction of the islands. The reasons for island formation may lie in the structural properties of the surfactant, such as the known strong intermolecular interactions of the alkanoic acids, or in the nature of the solvent and the interaction of the solute therewith.
(A1)
where Se is the total surface area, Γm is the maximum surface density of condensed molecules, V is the volume of the film islands, F is the density of the film, and M is the molecular weight of the film-forming molecules. With the volume of the film islands represented by V ) πr2h, eq A1 represents a linear first-order ODE and can be integrated along with the initial condition, r(t)ti) ) 0, to obtain an expression for the island radius as a function of time
[
{
}]
kd M kg (t - ti) r(t) ) 2h 1 - exp kd 2hF
(A2)
Back subsitution of eq A2 into eq A1, subject to the initial condition, Θf (t)ti) ) 0, results in a linear first-order ODE for Θf. With the following parameter definitions:
k2 ≡
kd M 2hF
kg r(tf∞) ≡ r∞ ) 2h kd
(A3) (A4)
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and
Θi ≡ or
πr∞2hF , for one island SeΓmM
Θi ≡ (A5a)
πr∞2 , for a monolayer of No nuclei. (A5b) Se
Integration of eq A1 results in eq 6 of the text. LA035732U
